Short answer: No, Aristotle was never captured by the Assyrians. The timeline alone makes it impossible.
The Assyrian Empire peaked centuries before Aristotle's birth. The Neo-Assyrian period—when Assyria dominated the Near East—ended with the fall of Nineveh in 612 BCE. Aristotle wasn't born until 384 BCE in Stagira, Greece, over two hundred years later. He lived, taught, and died (322 BCE) entirely within the Classical Greek world, later tutoring Alexander the Great.
They were a Semitic-speaking civilization centered on the city of Ashur (modern northern Iraq), rising to imperial power between the 10th and 7th centuries BCE. Their empire stretched from Egypt to Persia, famed for military innovation, brutal conquests, and the library of Ashurbanipal at Nineveh.
By Aristotle's time, the region once ruled by Assyria had passed through Babylonian, Persian, and Macedonian hands. Alexander's conquests (334–323 BCE) brought Greek culture eastward—but Aristotle himself never ventured beyond the Aegean world. His "empire" was intellectual: logic, biology, ethics, politics, and the Lyceum in Athens.
So while both shaped Western civilization—Assyria through imperial administration and written records, Aristotle through philosophy and science—their paths never crossed. Any tale of Aristotle in Assyrian chains is pure fiction.